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024 7 _a10.1088/978-0-7503-3759-5
_2doi
035 _a(CaBNVSL)thg00082710
035 _a(OCoLC)1275356606
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQC20.7.N6
_bF845 2021eb
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
082 0 4 _a530.155355
_223
100 1 _aFujimoto, Minoru,
_eauthor.
_970572
245 1 0 _aIntroduction to the mathematical physics of nonlinear waves /
_cMinoru Fujimoto.
250 _aSecond edition.
264 1 _aBristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
_bIOP Publishing,
_c[2021]
300 _a1 online resource (various pagings) :
_billustrations.
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _a[IOP release $release]
490 1 _aIOP ebooks. [2021 collection]
500 _a"Version: 202110"--Title page verso.
504 _aIncludes bibliographical references.
505 0 _a1. Nonlinearity and elliptic functions in classical mechanics -- 1.1. A pendulum -- 1.2. Vibration by a nonlinear spring force -- 1.3. Hyperbolic and elliptic functions -- 1.4. A jumping rope -- 1.5. Variation principle -- 1.6. Buckling of an elastic rod
505 8 _a2. Wave propagation, singularities, and boundary conditions -- 2.1. Elastic waves along a linear string in infinite length -- 2.2. Microwave transmission -- 2.3. Wave equations -- 2.4. Sound propagation in air -- 2.5. Asymptotic approximation in air space
505 8 _a3. Order variables for structural phase transitions -- 3.1. Symmetry group in crystals -- 3.2. Solitons and the Ising model for pseudospin correlations -- 3.3. Macroscopic views of structural phase transitions -- 3.4. Observing critical anomalies
505 8 _a4. Soft modes of lattice displacements -- 4.1. The Lyddane-Sachs-Teller relation -- 4.2. Soft modes in perovskite oxides -- 4.3. Dynamics of soft modes -- 4.4. Soft-mode frequency in modulated crystals -- 4.5. Optical studies on symmetry changes at critical temperature
505 8 _a5. Nonlinearity development in crystals : Korteweg-deVries' equation for collective order variables and the complex potential -- 5.1. The Korteweg-deVries equation -- 5.2. Thermal solution for the Weiss potential -- 5.3. Condensate pinning by the Weiss potential -- 5.4. Nonlinear waves and complex lattice potentials -- 5.5. The complex lattice potential -- 5.6. Isothermal phase transition and entropy production
505 8 _a6. Soliton mobility in time-temperature conversion for thermal processes : Riccati's theorem -- 6.1. Bargmann's theorem -- 6.2. Riccati's theorem and the modified Korteweg-deVries equation -- 6.3. Soliton mobility studied by computational analysis
505 8 _a7. Toda's lattice of correlation potentials -- 7.1. The Toda soliton lattice -- 7.2. Developing nonlinearity -- 7.3. Conversion to Korteweg-deVries' lattice potential
505 8 _a8. Scattering theory of the soliton lattice -- 8.1. Elemental waves -- 8.2. Scattering theory : dissipation, reflection, and transmission -- 8.3. Method of inverse scattering -- 8.4. Entropy production from soliton potentials
505 8 _a9. Pseudopotentials and sine-Gordon equation : topological correlations in domain structure -- 9.1. Pseudopotentials in mesoscopic phases -- 9.2. The sine-Gordon equation -- 9.3. Phase solitons in adiabatic processes -- 9.4. The B�acklund transformation and domain boundaries -- 9.5. Computational studies of the B�acklund transformation
505 8 _a10. Trigonal structural transitions : domain stability in topological order -- 10.1. The sine-Gordon equation -- 10.2. Observing adiabatic fluctuations -- 10.3. Toda's theory of domain stability -- 10.4. Kac's theory of nonlinearity for domain disorder -- 10.5. Domain separation and thermal and quasi-adiabatic transitions -- 10.6. Mesoscopic domains in topological disorder
505 8 _a11. Soliton theory of superconducting transitions -- 11.1. The Meissner effect and Fr�ohlich's proposal -- 11.2. Magnetic images of Fr�ohlich's interaction -- 11.3. The Cooper pair and persistent current -- 11.4. Critical temperatures and energy gap in superconducting transitions -- 11.5. Anderson's theory of superconducting phase transitions -- 11.6. Cuprate-layer structure and the Cooper pair -- 11.7. Meissner's effect in cuprate-layers and metallic hydrogen sulfide H3S
505 8 _a12. Irreducible thermodynamics of superconducting phase transitions -- 12.1. Superconducting phase transition -- 12.2. Electromagnetic properties of superconductors -- 12.3. The Ginzburg-Landau equation for superconducting phase transitions -- 12.4. Field theory of superconducting transitions.
520 3 _aWritten for students at upper-undergraduate and graduate levels, it is suitable for advanced physics courses on nonlinear physics. The book covers the fundamental properties of nonlinear waves, dealing with both theory and experiment. The aim is to emphasize established tools and introduce new methods underpinning important new developments in this field, especially as applied to solid-state materials. The updated edition has been extended to emphasize the importance of thermodynamics in a description of modulated crystals and contains new chapters on superconductivity that can be interpreted by the soliton mechanism. It is also updated to include new end-of-chapter problems.
521 _aGraduate students in physics and mathematical physics.
530 _aAlso available in print.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
545 _aMinoru Fujimoto is a retired professor from the University of Guelph, Canada, where he conducted research in the field of magnetic resonance studies on structural phase transitions in crystals which has currently been extended to theoretical work with soliton dynamics especially as applied to crystalline condensed matter systems. He is the author of numerous papers and several books including Physics of Classical Electromagnetism and Thermodynamics of Crystalline States (Springer); Introduction to Mathematical Physics of Nonlinear Waves and Solitons in Crystalline Processes (IOP Publishing). He lives in Mississauga, Ontario.
588 0 _aTitle from PDF title page (viewed on November 8, 2021).
650 0 _aNonlinear waves.
_93824
650 0 _aNonlinear theories.
_93339
650 7 _aMathematical physics.
_2bicssc
_911013
650 7 _aMathematics and computation.
_2bisacsh
_970439
710 2 _aInstitute of Physics (Great Britain),
_epublisher.
_911622
776 0 8 _iPrint version:
_z9780750337571
_z9780750337601
830 0 _aIOP (Series).
_pRelease 21.
_970573
830 0 _aIOP ebooks.
_p2021 collection.
_970574
856 4 0 _uhttps://iopscience.iop.org/book/978-0-7503-3759-5
942 _cEBK
999 _c82864
_d82864